Prepare the grill for indirect cooking over medium heat (350º-450ºF).
In a large cast iron skillet over direct heat, melt 1/3 cup of butter. Add the celery, onion, and garlic and cook until translucent, about 5 minutes. Stirring occasionally.
Add the flour to the skillet and stir until the liquid is absorbed.
Stir in the salt, pepper, celery seed, onion powder, and Italian seasoning.
Slowly whisk in the chicken broth and heavy cream. Cook until the sauce thickens, about 3–5 minutes. Remove from heat.
In a medium-sized cast iron skillet, add the sauce, then stir in the vegetables and turkey until evenly combined with the sauce.
Melt the remaining 1/3 cup of butter. Place a phyllo dough sheet across the top of the skillet, removing any that falls over the edge. Lightly brush the dough with butter. Repeat with the remaining dough.
Grill over indirect medium until the dough turns golden brown, approximately 40–50 minutes. Remove from the heat and serve.
